AbstractNumerizing and describing various sensations are important in the discussion of human information processings as well as in the construction of an information processing system, simulating human recognition and behavior. This paper considers the psychophysical function when the stimulus is multidimensional and the corresponding sensation is one‐dimensional. We define a state space spun by several physical continua and a psychological continuum, which is regarded as an n‐dimensional Riemannian space. the psychophysical function is defined as a certain geometrical invariant in this space. A metric is introduced into this state space based on the threshold of discrimination, and functions are derived which are permissible in this case as psychophysical functions. As an application of this formulation a problem is considered to establish a correspondence between the luminance and the brightness of the colored light. It is shown that when Weber's law and Ekman's law apply to the threshold of discrimination, Stiles' law and Abney's law can be derived as the permissible psychophysical functi